By generalizing Gessel-Xin's Laurent series method for proving the Zeilberger-Bressoud q-Dyson Theorem, we establish a family of qDyson style constant term identities. These identities give explicit formulas for certain coefficients of the q-Dyson product, including three conjectures of Sills' as special cases and generalizing Stembridge's first layer formulas for characters of SL(n, C).

We introduce an elementary method to give unified proofs of the Dyson, Morris, and Aomoto identities for constant terms of Laurent polynomials. These identities can be expressed as equalities of polynomials and thus can be proved by verifying them for sufficiently many values, usually at negative integers where they vanish. Our method also proves some special cases of the Forrester conjecture.

In this paper, the closed-form expressions for the coefficients of x 2 r x 2 s and x 2 r xsxt in the Dyson product are found by applying an extension of Good's idea. As consequences, we find several interesting Dyson style constant term identities.Mathematics Subject Classification. Primary 05A30, secondary 33D70.

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We give a short proof of Moll's minimal conjecture, which has been confirmed by Chen and Xia.